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Single Idea 15331

[filed under theme 3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms ]

Full Idea

If we abandon classical logic in favour of truth-value gaps and try to strengthen the theory, this leads to the Kripke-Feferman theory of truth, and variants of it.

Gist of Idea

Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength

Source

Leon Horsten (The Tarskian Turn [2011], 01.4)

Book Ref

Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.8

Related Idea

Idea 15330 Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten]

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The 6 ideas with the same theme [Kripke-Feferman axiomatisation of truth]:

16328

Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach]

15331

Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten]

16329

Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach]

16331

The KF is much stronger deductively than FS, which relies on classical truth [Halbach]

16332

The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]

19130

KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]